Year: 2026
Type: article
Abstract: We consider the two-species totally asymmetric simple exclusion process on $$\mathbb {Z}$$ Z with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along characteristic lines and prove the decay of the two-point functions in the large-time limit, thus confirming predictions of the nonlinear fluctuating hydrodynamics theory. Our approach builds on the queueing construction of the stationary measure introduced in [7, 32] and extends the theory of backwards paths for height functions developed in [14, 35]. The arguments for asymptotic decoupling also apply to further homogeneous initial data, and the decay of the two-point functions is proven for the stationary two-species asymmetric simple exclusion process, beyond the totally asymmetric case.
Authors: Patrik L. Ferrari, Sabrina Gernholt
Institution: University of Bonn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4417228517
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